Exclusive-OR function of single arborized neuron

We designed four arborized neurons which are able to evaluate the exclusive-or (XOR) function from two inputs. The input neurons form exclusively excitatory synapses on a dendritic tree which is a patchwork of "passive" (ohmic) and "active" cable segments. The active segments are described by the Hodgkin-Huxley model. The dynamics of the neurons and their output are obtained by numerical integration of the cable equation. In neurons 1 and 2 the XOR function is based on the annihilation of colliding action potentials. In neuron No. 3 the design takes advantage of the refractory period of action potentials. In neuron No. 4 voltage inversion is used as it occurs for inactivated sodium conductance in the Hodgkin-Huxley model. In all cases the XOR function depends critically on an appropriate timing of the input signals and on delays of the voltage transients in different branches of the dendrite.